Erickson&Whited (2000) Measurement Error and the Relationship Between Investment and q

Cash flow does not matter, even for financially con- strained firms, and despite its simple structure, g theory has good explanatory power once purged of measurement error.. Tobin 1969

Measurement Error and the Relationship

between Investment and q

Timothy Erickson

Bureau of Labor Statistics

Toni M Whited

University of Iowa

Many recent empirical investment studies have found that the in- vestment of financially constrained firms responds strongly to cash flow Paralleling these findings is the disappointing performance of the q theory of investment: even though marginal g should summarize the effects of all factors relevant to the investment decision, cash flow still matters We examine whether this failure is due to error in mea- suring marginal g Using measurement error—consistent generalized method of moments estimators, we find that most of the stylized facts produced by investment-q cash flow regressions are artifacts of mea-

surement error Cash flow does not matter, even for financially con-

strained firms, and despite its simple structure, g theory has good explanatory power once purged of measurement error

The effect of external financial constraints on corporate investment has been the subject of much research over the past decade Underlying

We gratefully acknowledge helpful comments from Lars Hansen, two anonymous ref-

erees, Serena Agoro-Menyang, Brent Moulton, John Nasir, Huntley Schaller, and partic- ipants of seminars given at the 1992 Econometric Society summer meetings, the University

of Pennsylvania, the University of Maryland, the Federal Reserve Bank of Philadelphia,

Rutgers University, and the University of Kentucky This paper was circulated previously

under the title “Measurement-Error Consistent Estimates of the Relationship between

Investment and Q.”

[Journal of Political Economy, 2000, vol 108, no 5]

© 2000 by The University of Chicago All rights reserved.0022-3808 / 2000 /10805-0003$02.50

this line of inquiry is the premise that informational imperfections in

equity and credit markets lead to a divergence between the costs of external and internal funds or, at the extreme, to rationing of external finance Any difficulties the firm faces in obtaining outside financing then affect its real investment decisions Recent interest in this topic started with Fazzari, Hubbard, and Petersen (1988), who showed em-

pirically that for groups of firms perceived a priori to face financing

constraints, investment responds strongly to movements in internal

funds, even after one controls for investment opportunities Hubbard

(1998) cites numerous studies that have confirmed these results This literature is the most prominent example of the empirical failure of the

neoclassical intertemporal optimization model of investment

Most tests of the neoclassical model and most empirical studies of

the interaction of finance and investment are based on what is com- monly referred to as the q theory of investment Despite its repeated failure to explain both cross-section and time-series data, its popularity

persists because of its intuitive appeal, simplicity, and sound theoretical

underpinnings Its popularity persists also because of conjectures that its empirical failure is spurious, a consequence of measurement error

in q In recent years, however, a number of studies that explicitly address

measurement error have reaffirmed the earlier findings, particularly that

of a significant role for internal funds (see, e.g., Blundell et al 1992:

Gilchrist and Himmelberg 1995) In the present paper we employ a very different approach to the measurement error problem and come

to very different conclusions

To understand the measurement error problem, it is crucial to think

carefully about ¢ theory The intuition behind this theory can be found

in Keynes (1936): “there is no sense in building up a new enterprise at

a cost greater than that at which a similar existing enterprise can be purchased; whilst there is an inducement to spend on a new project what may seem an extravagant sum, if it can be floated off the stock exchange at an immediate profit” (p 151) Grunfeld (1960) argued

similarly that a firm should invest when it expects investment to be

profitable and that an efficient asset market’s valuation of the firm captures this expectation He supported this reasoning by finding that firm market value is an important determinant of investment in a sample

of U.S firms Tobin (1969) built on this work by using a straightforward arbitrage argument: the firm will invest if Tobin’s g, the ratio of the market valuation of a firm’s capital stock to its replacement value, ex- ceeds one Modern q theory is based on the first-order conditions in Lucas and Prescott (1971) and Mussa (1977) that require the marginal adjustment and purchase costs of investing to be equal to the shadow value of capital Termed marginal q¢, this shadow value is the firm man-

ager’s expectation of the marginal contribution of new capital goods to future profit

Testing this first-order condition typically relies on drawing a con- nection between the formal optimization model and the intuitive ar

guments of Keynes, Grunfeld, and Tobin For most researchers, the first

step in making this connection is to assume quadratic investment ad-

justment costs, which gives a first-order condition that can be rearranged

as a linear regression in which the rate of investment is the dependent variable and marginal q is the sole regressor The next step is to find

an observable counterpart to marginal g Building on results in Lucas

and Prescott (1971), Hayashi (1982) simplified this task by showing that

constant returns to scale and perfect competition imply the equality of marginal q with average q, which is the ratio of the manager’s valuation

of the firm’s existing capital stock to its replacement cost If financial markets are efficient, then their valuation of the capital stock equals the manager’s, and consequently, average g should equal the ratio of this market valuation to the replacement value, that is, Tobin’s g In

principle, Tobin’s g is observable, though in practice its measurement

presents numerous difficulties

The resulting empirical models have been disappointing along several dimensions.' The R’’s are very low, suggesting that marginal q has little

explanatory power Further, many authors argue (incorrectly, as we show

below) that the fitted models imply highly implausible capital stock adjustment costs and speeds Finally, the theoretical prediction that mar- ginal g should summarize the effects of all factors relevant to the in-

vestment decision almost never holds: output, sales, and, as emphasized

above, measures of internal funds typically have statistically significant coefficient estimates and appreciable explanatory power if they are in-

troduced as additional regressors In particular, estimates of the coef- ficient on cash flow (the most common measure of internal funds) are

typically larger and more significant for firms deemed to be financially constrained than for firms that are not

These results have a variety of interpretations If measured Tobin’s ¢

is a perfect proxy for marginal g and the econometric assumptions are

correct, then, roughly speaking, ¢ theory is “wrong.” In other words, a

manager’s profit expectations do not play an important role in explain- ing investment, but internal funds apparently do Alternatively, if ¿ the-

ory is “correct” and measured Tobin’s g is a perfect proxy, then some

of the econometric assumptions are wrong For example, Hayashi and Inoue (1991) consider endogeneity of marginal g, and Abel and Eberly 'See Ciccolo (1975), Summers (1981), Abel and Blanchard (1986), and Blanchard, Rhee, and Summers (1993) for studies using aggregate data Recent micro studies include Fazzari et al (1988), Schaller (1990), Blundell et al (1992), and Gilchrist and Himmelberg (1995)

(1996) and Barnett and Sakellaris (1998) consider nonlinear regression

A third possibility is that g theory and the econometric assumptions are

correct, but measured Tobin’s g is a poor proxy for marginal ¢

Mismeasurement of marginal q can generate all the pathologies af-

flicting empirical g models In the classical errors-in-variables model, for example, the ordinary least squares (OLS) R° is a downward-biased

estimate of the true model’s coefficient of determination, and the OLS

coefficient estimate for the mismeasured regressor is biased toward zero Irrelevant variables may appear significant since coefficient estimates for perfectly measured regressors can be biased away from zero This

bias can differ greatly between two subsamples, even if the rate of mea- surement error is the same in both The spurious-significance problem

is exacerbated by the fact that homoskedastic measurement error can

generate conditionally heteroskedastic data, thus inappropriately shrink-

ing OLS standard errors Finally, the conditional expectation of the

independent variable given the proxy is generally nonlinear, which may lead to premature abandonment of linear functional forms.”

Other explanations for the failure of investment-¢ regressions, such

as finance constraints, fixed costs, learning, or simultaneity bias, are appealing but, unlike the measurement error hypothesis, cannot indi- vidually explain all of ¢ theory’s empirical shortcomings It therefore is

natural to try an explicit errors-in-variables remedy Papers doing so

include Abel and Blanchard (1986), Hoshi and Kashyap (1990), Blhun- dell et al (1992), Cummins, Hassett, and Hubbard (1994), Gilchrist and Himmelberg (1995), and Cummins, Hassett, and Oliner (1998) For the most part, these papers find significant coefficients on measures

of internal funds Notably, Gilchrist and Himmelberg find, like Fazzari

et al., that for most ways of dividing their sample into financially con- strained and unconstrained firms, the constrained firms’ investment is more sensitive to cash flow

We use a very different method Following Geary (1942), we construct

consistent estimators that use the information contained in the third-

and higher-order moments of the joint distribution of the observed

regression variables By using generalized method of moments (GMM) (Hansen 1982) to exploit the information afforded by an excess of moment equations over parameters, we increase estimator precision and obtain the GMM ftest of overidentifying restrictions as a tool for de- tecting departures from the assumptions required for estimator consistency

The results from applying OLS and GMM estimators to our data on U.S manufacturing firms both cast doubt on the Fazzari et al (FHP) hypothesis: that the investment of liquidity-constrained firms responds

“See Gleser (1992) for a discussion of this last point

strongly to cash flow As expected, the OLS regression of investment on measured Tobin’s g gives an unsatisfyingly low R* and a significantly

positive estimate for the coefficient on cash flow However, the estimated

cash flow coefficient is much greater for firms classified as uncon-

strained, the reverse of what is predicted by the FHP hypothesis This reverse pattern has been observed before in the literature and, like the

expected pattern, can be explained in terms of measurement error

In contrast, our GMM estimates of the cash flow coefficient are small

and statistically insignificant for subsamples of a priori liquidity-con- strained firms as well as subsamples of unconstrained firms Further- more, the GMM estimates of the population F’ for the regression of investment on true marginal gare, on average, more than twice as large

as the OLS R’ Similarly, the GMM estimates of the coefficient on mar- ginal gare much larger than our OLS estimates, though, as noted above,

we shall argue that these coefficients are not informative about adjust-

ment costs Measurement error theory predicts these discrepancies, and,

in fact, we estimate that just over 40 percent of the variation in measured Tobin’s q is due to true marginal ¢

We organize the paper as follows Section II reviews ¢ theory, estab- lishes criteria for its empirical evaluation, and describes likely sources

of error in measuring marginal g Section II presents our estimators and discusses their applicability to ¢ theory Section IV reports our es- timates Section V explains how a measurement error process that is the same for both constrained and unconstrained firms can generate spurious cash flow coefficient estimates that differ greatly between these two groups The construction of our data set and Monte Carlo simu- lations of our estimators are described in Appendices A and B

II A Simple Investment Model

To provide a framework for discussing specification issues concerning our empirical work, we present a standard dynamic investment model

in which capital is the only quasi-fixed factor and risk-neutral managers choose investment each period to maximize the expected present value

of the stream of future profits The value of firm ¿ at time ¢ is given by

manager of firm at time 4 6, is the firm’s discount factor at time 6 K,

is the beginning-of-period capital stock; /, is investment; H(K,, &,,) 1s the profit function, II, >0; and WU, K,, ¥» hj) is the investment adjust- ment cost function, which is increasing in /,, decreasing in K,, and

convex in both arguments The term h, is a vector of variables, such as labor productivity, that might also affect adjustment costs, and £, and

v, are exogenous shocks to the profit and adjustment cost functions;

both are observed by the manager but unobserved by the econometri- cian at time ¢ All variables are expressed in real terms, and the relative price of capital is normalized to unity Note that any variable factors of

production have already been maximized out of the problem

The firm maximizes equation (1) subject to the following capital stock accounting identity:

where d, is the assumed constant rate of capital depreciation for firm

2 Let x, be the sequence of Lagrange multipliers on the constraint (2) The first-order condition for maximizing the value of the firm in equa-

Equation (3) states that the marginal cost of investment equals its ex-

pected marginal benefit The left side comprises the adjustment and purchasing costs of capital goods, and the right side represents the

expected shadow value of capital, which, as shown in (4), 1s the expected stream of future marginal benefits from using the capital These benefits include both the marginal additions to profit and reductions in instal-

lation costs Since we normalize the price of capital goods to unity, x,,

is the quantity “marginal q¢’ referred to in the Introduction

Most researchers to date have tested ¢ theory via a linear regression

of the rate of investment on x, This procedure requires a proxy for the unobservable x,,and a functional form for the installation cost func- tion having a partial derivative with respect to /, that is linear in L/K,, and v, Below we consider at length the problem of obtaining a

proxy A class of functions that meets the functional form requirement

and is also linearly homogeneous in J, and K,, is given by

Ii

it

Here, fis an integrable function, and a,, ., @, are constants We re-

strict a, >0 to ensure concavity of the value function in the maximi- zation problem The adjustment cost functions chosen either explicitly

or implicitly by all researchers who test g theory with linear regressions are variants of (5) Differentiating (5) with respect to J, and substituting

the result into (3) yields the familiar regression equation

—as9,/2q;

To evaluate this model, most authors regress y,,on a proxy for x,, usually

a measure of Tobin’s g, and then do one or more of the following three things: (i) examine the adjustment costs implied by estimates of 8; (ii) examine the explanatory power of x;, as measured by the R® of the fitted model; and (iii) test whether other variables enter significantly into the fitted regression, since theory says that no variable other than

Xz Should appear in (6) Some authors split their samples into subsam- ples consisting of a priori financially constrained and unconstrained

firms and then perform these evaluations, especially point iii, separately

on each subsample

In the present paper we estimate financially constrained and uncon- strained regimes by fitting the full sample to models that interact cash

flow with various financial constraint indicators We perform measure-

ment error—consistent versions of points ii and iii We ignore point i because any attempt to relate 6 to adjustment costs contains two serious pitfalls First, equation (3) implies that a firm’s period ¢ marginal ad- justment costs are identically equal to x,,— 1 and are therefore inde- pendent of 8 Second, the regression equation (6) cannot be integrated back to a unique adjustment cost function but to a whole class of func-

tions given by (5) Any attempt at evaluating a firm’s average adjustment costs, ¥/I,, requires a set of strong assumptions to choose a function from this class, and different arbitrary choices yield widely different

estimates of adjustment costs.’ Note that the constant of integration should not be interpreted as a fixed cost since it does not necessarily

* See Whited (1994) for further discussion and examples,

“turn off’ when investment is zero It can, however, be interpreted as a

permanent component of the process of acquiring capital goods, such

as a purchasing department

We now show how attempts to use Tobin’s g to measure marginal ¿ can admit serious error To organize our discussion we use four quantities

The first is marginal g, defined previously as x, The second is average

q, defined as V,/K,, where the numerator is given by (1); recall that V,

is the manager’s subjective valuation of the capital stock The third is

Tobin’s g, which is the financial market’s valuation of average g Con-

ceptual and practical difficulties exist in measuring the components of Tobin’s g; we therefore introduce a fourth quantity called measured q,

defined to be an estimate of Tobin’s ¢ Measured q is the regression proxy for marginal g; average q and Tobin’s q are simply devices for identifying and assessing possible sources of error in measuring marginal

These sources can be placed in three useful categories, corresponding

to the possible inequalities between successive pairs of the four concepts

of q First, marginal g may not equal average q, which will occur whenever

we have a violation of the assumption either of perfect competition or

of linearly homogeneous profit and adjustment cost functions A second

source of measurement error is divergence of average q from Tobin's

q As discussed in Blanchard et al (1993), stock market inefficiencies

may cause the manager’s valuation of capital to differ from the market

valuation Finally, even if marginal g equals average gq and financial markets are efficient, numerous problems arise in estimating Tobin’s g Following many researchers in this area, we estimate Tobin’s q¢ by eval- uating the commonly used expression

dD, + Si ~~ Ni

x

i

Here D,, is the market value of debt, S, is the market value of equity, N,

is the replacement value of inventories, and K, is redefined as the re- placement value of the capital stock Note that the numerator only approximates the market value of the capital stock The market values

of debt and equity equal the market value of the firm, so the market

value of the capital stock is correctly obtained by subtracting adi other assets backing the value of the firm: not just the replacement value of inventories, but also the vatue of non-physical assets such as human capital and goodwill The latter assets typically are not subtracted be- cause data limitations make them impossible to estimate An additional

source of error is that D,, N,, and K, must be estimated from accounting

data that do not adequately capture the relevant economic concepts

As is typical of the literature, we estimate these three variables using

recursive procedures; details can be found in Whited (1992) An alter- native method of constructing K, that addresses the problem of capital aggregation is given by Hayashi and Inoue (1991)

From this discussion it is clear that the measurement errors are serially correlated because market power persists over time, because deviations

of market expectations from fundamental value are subject to persistent

“fads,” and because the procedures used to approximate the compo- nents of (7) directly induce serial correlation in its measurement error

These procedures use a previous period’s estimate of a variable to cal-

culate the current period’s estimate, implying that the order of serial correlation will be at least as great as the number of time-series obser- vations This type of correlation violates the assumptions required by

the measurement error remedies used in some of the papers cited in the Introduction As shown below, however, our own estimators permit

virtually arbitrary dependence

Our data set consists of 737 manufacturing firms from the Compustat database covering the years 1992-95 Our sample selection procedure

is described in Appendix A, and the construction of our regression variables is described in the appendix to Whited (1992) Initially we treat this panel as four separate (but not independent) cross sections

We specify an errors-in-variables model, assume that it holds for each cross section, and then compute consistent estimates of each cross sec-

tion’s parameters using the estimators we describe below Assuming that the parameters of interest are constant over time, we next pool their

cross-section estimates using a minimum distance estimator, also de- scribed below

A — Cross-Section Assumptions

For convenience we drop the subscript f and rewrite equation (6) more

generally as

For application to a split sample consisting only of a priori financially

constrained (or unconstrained) firms, z, is a row vector containing

Z = 1 and z, = (cash flow),/K, For application to a full sample, z, further includes z, = dz, and z,, = d, where d, = 1 if firm 7 is finan-

cially constrained and d; = 0 otherwise We assume that u, is a mean zero error independent of (z, x,) and that x; is measured according to

where x, is measured g and e, is a mean zero error independent of (x,

Zz, X,) The intercept +¿ allows for the nonzero means of some sources

of measurement error, such as the excess of measured g over Tobin's ø

caused by unobserved non-physical assets Our remaining assumptions

are that (us €, 213 20: ZX), = 1, ., ”, are independently and iden-

tically distributed (i.i.d.), that the residual from the projection of x, on

z, has a skewed distribution, and that 8 # 0 The reason for the last two assumptions and a demonstration that they are testable are given in subsection B

There are two well-known criticisms of equation (8) and its accom-

panying assumptions First, the relationship between investment and

marginal q (i.e., between y, and x,) may be nonlinear As pointed out

by Abel and Eberly (1996) and Barnett and Sakellaris (1998), this prob- lem may occur when there are fixed costs of adjusting the capital stock These papers present supporting empirical evidence; recall, however, that a linear measurement error model can generate nonlinear con-

ditional expectation functions in the data, implying that such evidence

is ambiguous

The second well-known criticism is that u,; may not be independent

of (z, x,) because of the simultaneous-equations problem The possible dependence between u, and x, arises because the “regression” (6) un- derlying (8) is a rearranged first-order condition Recalling that wu, is

inversely related to v,, note that v,, does not appear in (4), the expression

giving x, This absence is the result of our one-period time to build assumption To the extent that this assumption holds, therefore, v, can

be related to x, only indirectly One indirect route is the effect of », on

K.,., /2 1, and thence on the future marginal revenue product of cap-

ital This route is blocked if we combine our linearly homogeneous adjustment cost function with the additional assumptions of (i) perfect competition and (ii) linearity of the profit function in K;,,; The other indirect route is temporal dependence between z„ and 9,,., =

Wj Ee hy,.,), 721 This route can be blocked by a variety of as- sumption sets such as the following: (ilia) @„ 1s independent of ¢,,,, for

2 1; or (iiib) v, is independent of €, for all 4, and the function f ap- pearing in (5) is identically zero Note that conditions i and ii, which are necessary, also eliminate the divergence of marginal from average

g Our estimates will be valuable, then, to the extent that measurement error is large, but mostly because of the other sources discussed in Section ITB

The possible dependence between u, and the cash flow ratio, 2, occurs

if current investment typically becomes productive, cash flow—producing

capital within the period, a violation of our one-period time to build

assumption Other possible elements of z; are dummy variables indi- cating the presence of liquidity constraints and the interactions of these

dummies with z, One dummy identifies firms lacking a bond rating; the other dummy identifies “small” firms We argue below that firm size

and bond ratings are independent of x,

We also see a noteworthy problem with our measurement error as- sumptions: they ignore mismeasurement of the capital stock If capital

is mismeasured, then, since it is the divisor in the investment rate Vo the proxy x, and the cash flow ratio z,, these ratios are also mismeasured,

with conditionally heteroskedastic and mutually correlated measure- ment errors

It is clear that the criticized assumptions may not hold However, only

assumption violations large enough to qualitatively distort inferences are a problem In Appendix B we present Monte Carlo simulations showing that it is possible to detect such violations with the GMM ftest

of overidentifying restrictions

B — Cross-Section Estimators

To simplify our computations we first “partial out” the perfectly mea-

sured variables in (8) and (9) and rewrite the resulting expressions in

terms of population residuals This yields

and

where

(Hy Be By) = [E@z,)]”'E[z2@, x„ x2]

and 9; = x;— z;w„ Given (p,, w,), this is the textbook classical errors- in-variables model, since our assumptions imply that u, ¢, and +, are

mutually independent Substituting

(i, a) = (Saez) X z0 xì i=] 1=1

into (10) and (11), we estimate 8, E(u?), E(e?), and E(y?) with the GMM

procedure described in the next paragraph Estimates of the [th element

of @ are obtained by substituting the GMM estimate of 8 and the Ah elements of ñ, and â, into

œ, = py — BB, se 0 (12) Estimates of p? = 1 — [Var (u,)/ Var (y,)], the population R° for (8), are obtained by evaluating

ty Var (z)p, + EIn?\8”

Em Var(z)g, + Eln?)8° + Elsil (19)

at #,, #,, the sample covariance matrix for z, and the GMM estimates

of 6, E(y?), and E(u?)

Our GMM estimators are based on equations expressing the moments

of y, ~ zp, and x, — 2,4, as functions of 8 and the moments of u, €, and

n, There are three second-order moment equations:

EQ@, — zw,)”] = 8°E@) + E0), (14) ElQ, — z,w,)(x,— #,w)] = BEG) (15)

and

E[(x,— zw)”]Ì = E7) + E()) (16)

The left-hand-side quantities are consistently estimable, but there are

only three equations with which to estimate the four unknown param- eters on the right-hand side The third-order product moment equa-

tions, however, consist of two equations in two unknowns:

El(y, — 2p)" (x, — zie] = BEM?) (17)

and

E[Q, — z,w,)(x,T— z,0)°] = BE(n?) (18)

Geary (1942) was the first to point out the possibility of solving these two equations for 6 Note that a solution exists if the identifying as- sumptions 8 # 0 and E(y;) # 0 are true, and one can test the contrary hypothesis 6 = 0 or E(y?) = 0 or both by testing whether the sample counterparts to the left-hand sides of (17) and (18) are significantly different from zero

Given 8, equations (14)-(16) and (18) can be solved for the remain- ing right-hand-side quantities We obtain an overidentified equation system by combining (14)-(18) with the fourth-order product moment equations, which introduce only one new quantity, E(n;):

EG, — 2.6) (x, — Zp) = 8”EA) + 38E(@)E02) (19)

Le

~ > (0, - 24)" — [8°B(n?) + Bou?)

= lọ, — z8,)œ&, — #8,)”] — 8[E() + 3E(?)E(?)]

where the matrix of the quadratic form is chosen to minimize asymptotic variance This matrix differs from the standard optimal weighting matrix

by an adjustment that accounts for the substitution of (#,, ~,) for (#, #,); see Erickson and Whited (1999) for details

Although the GMM estimator just described efficiently utilizes the

information contained in equations (14)—(21), nothing tells us that this

system is an optimal choice from the infinitely many moment equations available We therefore report the estimates obtained from a variety of equation systems; as will be seen, the estimates are similar and support

the same inference We use three specific systems: (14 )-(18), (14)-(21), and a larger system that additionally includes the equations for the fifth-

order product moments and the third-order non—product moments We

denote estimates from these nested systems as GMM3, GMM4, and

GMM5.°

Along with estimates of @,, a, 8, and p”, we shall also present estimates

of r* = 1 — [Var (€,)/ Var (y,)], the population R’ for (9) This quantity

is a useful index of measurement quality: the quality of the proxy variable

x, ranges from worthless at 7* = 0 to perfect at 7? = 1 We estimate 7°

in a way exactly analogous to that for p’

The asymptotic distributions for all the estimators of this section can

be found in Erickson and Whited (1999)

C Identification and the Treatment of Fixed Effects

Transforming the observations for each firm into deviations from that firm’s four-year averages or into first differences is a familiar preventive remedy for bias arising when fixed effects are correlated with regressors

* Cragg (1997) gives an estimator that, apart from our adjustment to the weighting matrix, is the GMM4 estimator

For our data, however, after either transformation we can find no evi- dence that the resulting models satisfy our identifying assumptions

8 #0 and EM?) # 0: the hypothesis that the left-hand sides of (17) and (18) are both equal to zero cannot be rejected at even the 1 level, for any year and any split-sample or full-sample specification.” In fact, the great majority of the pvalues for this test exceed 4 In contrast, untransformed (levels) data give at least some evidence of identification

with splicsample models and strong evidence with the interaction term

models; see tables 1 and 2 below We therefore use data in levels form Our defense against possible dependence of a fixed effect in wu, (or €,)

on (z, x,) is the ftest The test will have power to the extent that the dependence includes conditional heteroskedasticity (which is simulated

in App B), conditional skewness, or conditional dependence on other

high-order moments

Let y denote any one of our parameters of interest: a, a, B, 0”, OF 7”

Suppose that y,, ., ¥, are the four cross-section estimates of y given

by any one of our estimators An estimate that is asymptotically more

efficient than any of the individual cross-section estimates is the value

minimizing a quadratc form in (Ÿ, — +, , 3 — y), Where the matrix

of the quadratic form is the inverse of the asymptotic covariance matrix

of the vector (y, , ¿) Newey and McFadden (1994) call this a clas-

sical minimum distance estimator A nice feature of this estimator is that it does not require assuming that the measurement errors €,, are

serially uncorrelated."

For each parameter of interest we compute four minimum distance

estimates, corresponding to the four types of cross-section estimates:

OLS, GMM3, GMM4, and GMM5 To compute each minimum distance estimator, we need to determine the covariances between the cross- section estimates being pooled Our estimate of each such covariance

is the covariance between the estimators’ respective influence functions (see Erickson and Whited 1999)

* The liquidity constraint criteria “firm size” and “bond rating” are defined in Sec IV

The Wald statistic used for these tests, based on the sample counterparts to the left-hand

sides of (17) and (18), is given in Erickson and Whited (1999) The intercept is deleted

from a, the vector z, is redefined to exclude z, = 1, and ¥, is eliminated from (9) when

we fit models to transformed data

° We can also pool four estimates of the entire vector of parameters of interest, (a, O,

G, o°, 7°), obtaining an asymptotic efficiency gain like that afforded by seemingly unrelated

regressions However, this estimator performs unambiguously worse in Monte Carlo sim-

ulations than the estimators we use, probably because the 20 x 20 optimal minimum

distance weighting matrix is too large to estimate effectively with a sample of our size

E Previous Approaches

It is useful to note how the measurement error remedies used by other

authors differ from our own One alternative approach is to assume that ¢, is serially uncorrelated, thereby justifying the estimators of Gril-

iches and Hausman (1986) or the use of lagged values of measured đụ

as instruments Studies doing so are those by Hoshi and Kashyap (1990),

Blundell et al (1992), and Cummins, Hassett, and Hubbard (1994) As

noted, however, a substantial intertemporal error correlation is highly

likely Another approach is that of Abel and Blanchard (1986), who

proxy marginal q by projecting the firm’s series of discounted marginal

profits onto observable variables in the firm manager’s information set Feasible versions of this proxy, however, use estimated discount rates and profits, creating a measurement error that can be shown to have

deleterious properties similar to those in the classical errors-in-variables model For example, Gilchrist and Himmelberg (1995), who adapt this approach to panel data, assume one discount rate for all firms and time

periods; insofar as the true discount rates are correlated with cash flow, this procedure creates a measurement error that is correlated with the proxy Finally, a third alternative approach is that of Cummins, Hassett, and Oliner (1998), who proxy marginal g by a discounted series of

financial analysts’ forecasts of earnings

Much of the recent empirical ¢ literature has emphasized that groups

of firms classified as financially constrained behave differently than those

that are not In particular, many studies have found that cash flow enters

significantly into investment-g regressions for groups of constrained firms, a result that has been interpreted as implying that financial market imperfections cause firm-level investment to respond to movements in

internal funds In addressing this issue, we need to tackle two prelim- inary matters First, we need to find observable variables that serve to separate our sample of firms into financially constrained and uncon- strained groups Second, we need to see whether our estimators can

perform well on these subsamples

The investment literature has studied a number of indicators of po- tential financial weakness For example, Fazzari et al (1988) use the

dividend payout ratio, arguing that dividends are a residual in the firm’s real and financial decisions Therefore, a firm that does not pay divi- dends must face costly external finance; otherwise it would have issued

new shares or borrowed in order to pay dividends Whited (1992) clas- sifies firms according to whether they have bond ratings or not The intuition here is that a firm with a bond rating has undergone a great